101. A motion has position equation \(x=5-3t\), where \(x\) is in \( \text{m} \) and \(t\) is in \( \text{s} \). The motion is best described as
ⓐ. uniform motion with velocity \(-3\,\text{m s}^{-1}\)
ⓑ. uniform motion with velocity \(+5\,\text{m s}^{-1}\)
ⓒ. rest at \(x=5\,\text{m}\)
ⓓ. uniformly accelerated motion with acceleration \(-3\,\text{m s}^{-2}\)
Correct Answer: uniform motion with velocity \(-3\,\text{m s}^{-1}\)
Explanation: The standard constant-velocity form is
\[
x=x_0+vt
\]
The given equation is
\[
x=5-3t
\]
Comparing the two equations, the initial position is
\[
x_0=5\,\text{m}
\]
The coefficient of \(t\) is the velocity:
\[
v=-3\,\text{m s}^{-1}
\]
Since the coefficient of \(t\) is constant, the velocity is constant.
The negative sign means the position coordinate decreases with time.
\( \textbf{Final answer:} \) The body has uniform motion with velocity \(-3\,\text{m s}^{-1}\).
102. A car covers equal displacements of \(15\,\text{m}\) in every \(3\,\text{s}\) interval along the same direction. Its acceleration is
ⓐ. \(0\,\text{m s}^{-2}\)
ⓑ. \(3\,\text{m s}^{-2}\)
ⓒ. \(5\,\text{m s}^{-2}\)
ⓓ. \(15\,\text{m s}^{-2}\)
Correct Answer: \(0\,\text{m s}^{-2}\)
Explanation: Equal displacements in equal time intervals along the same direction indicate constant velocity. The velocity in each interval is
\[
v=\frac{15\,\text{m}}{3\,\text{s}}=5\,\text{m s}^{-1}
\]
Since this velocity does not change from one interval to the next, the change in velocity is zero.
Acceleration is the rate of change of velocity.
So,
\[
a=0\,\text{m s}^{-2}
\]
The value \(5\,\text{m s}^{-1}\) is velocity, not acceleration.
\( \textbf{Final answer:} \) The acceleration is \(0\,\text{m s}^{-2}\).
103. Assertion: A body moving with constant velocity has zero acceleration.
Reason: Acceleration measures the rate of change of velocity with time.
ⓐ. Both Assertion and Reason are true, and Reason explains Assertion
ⓑ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓒ. Assertion is true, but Reason is false
ⓓ. Assertion is false, but Reason is true
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: Constant velocity means that velocity does not change with time. Acceleration is connected with change in velocity per unit time. If the change in velocity is zero over every time interval, the acceleration is \(0\,\text{m s}^{-2}\). The Reason states the exact principle used to understand the Assertion. This remains true even if the constant velocity is negative, because negative constant velocity still has no change in velocity.
104. For a body obeying \(x=x_0+vt\), doubling the time interval while keeping \(v\) constant will double
ⓐ. the acceleration during that interval
ⓑ. the initial position \(x_0\)
ⓒ. the unit of velocity
ⓓ. the displacement during that interval
Correct Answer: the displacement during that interval
Explanation: For constant velocity, displacement during time \(t\) is \(s=vt\). If \(v\) remains constant, displacement is directly proportional to time. Doubling \(t\) changes \(vt\) to \(v(2t)=2vt\), so the displacement doubles. The initial position \(x_0\) is fixed by where the body was at \(t=0\,\text{s}\). Acceleration remains zero for constant velocity, and units do not change when the time interval is changed.
105. A straight-line \(x-t\) graph has a constant negative slope. The motion represented is
ⓐ. rest at a negative coordinate
ⓑ. uniform motion in the negative direction
ⓒ. non-uniform motion with increasing speed
ⓓ. motion with zero displacement in every interval
Correct Answer: uniform motion in the negative direction
Explanation: On an \(x-t\) graph, the slope gives velocity. A straight line has constant slope, so the velocity is constant. If the slope is negative, the position coordinate decreases with time. This means the body moves in the negative direction with uniform velocity. A horizontal line would represent rest, while a curved graph would show changing velocity.
106. A body follows \(x=12-4t\), where \(x\) is in \( \text{m} \) and \(t\) is in \( \text{s} \). Its displacement from \(t=1\,\text{s}\) to \(t=4\,\text{s}\) is
ⓐ. \(+12\,\text{m}\)
ⓑ. \(-12\,\text{m}\)
ⓒ. \(+16\,\text{m}\)
ⓓ. \(-16\,\text{m}\)
Correct Answer: \(-12\,\text{m}\)
Explanation: \( \textbf{Position function:} \)
\[
x=12-4t
\]
At \(t=1\,\text{s}\),
\[
x_1=12-4(1)=8\,\text{m}
\]
At \(t=4\,\text{s}\),
\[
x_2=12-4(4)=-4\,\text{m}
\]
Displacement is
\[
\Delta x=x_2-x_1
\]
\[
\Delta x=-4\,\text{m}-8\,\text{m}
\]
\[
\Delta x=-12\,\text{m}
\]
The negative sign matches the negative constant velocity in the equation.
\( \textbf{Final answer:} \) The displacement is \(-12\,\text{m}\).
107. For a body moving with constant velocity, displacement is directly proportional to time because
ⓐ. acceleration increases uniformly with time
ⓑ. distance is always equal to zero
ⓒ. velocity remains fixed while time changes
ⓓ. the origin moves with the body
Correct Answer: velocity remains fixed while time changes
Explanation: For constant velocity, the displacement in time \(t\) is given by \(s=vt\). If \(v\) remains fixed, then \(s\) changes in the same ratio as \(t\). For example, doubling the time doubles the displacement, provided the velocity is unchanged. This proportionality does not require acceleration; in fact, acceleration is zero for constant velocity. The origin is only a reference point and does not cause the proportional relation.
108. Study the position table for a moving object.
| Time | Position |
|---|
| \(0\,\text{s}\) | \(18\,\text{m}\) |
| \(2\,\text{s}\) | \(12\,\text{m}\) |
| \(4\,\text{s}\) | \(6\,\text{m}\) |
| \(6\,\text{s}\) | \(0\,\text{m}\) |
The motion is best described as
ⓐ. uniform motion with velocity \(-3\,\text{m s}^{-1}\)
ⓑ. uniform motion with velocity \(+3\,\text{m s}^{-1}\)
ⓒ. non-uniform motion with increasing positive velocity
ⓓ. rest at different positions
Correct Answer: uniform motion with velocity \(-3\,\text{m s}^{-1}\)
Explanation: In each \(2\,\text{s}\) interval, the position decreases by \(6\,\text{m}\). Equal displacements occur in equal time intervals, so the velocity is constant. The velocity is
\[
v=\frac{\Delta x}{\Delta t}
\]
\[
v=\frac{-6\,\text{m}}{2\,\text{s}}=-3\,\text{m s}^{-1}
\]
The negative sign shows that the motion is in the negative direction. The object is not at rest because its position changes with time.
\( \textbf{Final answer:} \) The motion is uniform with velocity \(-3\,\text{m s}^{-1}\).
109. Non-uniform motion is indicated when a body
ⓐ. has the same coordinate at all instants
ⓑ. has unequal displacements in equal intervals
ⓒ. has equal displacements in equal intervals
ⓓ. has a fixed origin chosen for coordinates
Correct Answer: has unequal displacements in equal intervals
Explanation: Non-uniform motion means the velocity is not constant. In one-dimensional motion, this is often seen when a body covers unequal displacements in equal time intervals. The body may be speeding up, slowing down, or changing direction. A fixed origin is needed to describe position, but it does not decide whether motion is uniform or non-uniform. Equal displacements in equal time intervals would instead indicate uniform velocity.
110. A trolley has the following position record.
| Time | Position |
|---|
| \(0\,\text{s}\) | \(0\,\text{m}\) |
| \(1\,\text{s}\) | \(2\,\text{m}\) |
| \(2\,\text{s}\) | \(7\,\text{m}\) |
| \(3\,\text{s}\) | \(15\,\text{m}\) |
What does the table show?
ⓐ. Uniform motion with \(2\,\text{m s}^{-1}\)
ⓑ. Uniform motion with \(5\,\text{m s}^{-1}\)
ⓒ. Non-uniform motion; displacements increase
ⓓ. Rest with the same position in each interval
Correct Answer: Non-uniform motion; displacements increase
Explanation: The time intervals are equal, each being \(1\,\text{s}\). The displacement from \(0\,\text{s}\) to \(1\,\text{s}\) is \(2\,\text{m}\). The displacement from \(1\,\text{s}\) to \(2\,\text{s}\) is \(5\,\text{m}\). The displacement from \(2\,\text{s}\) to \(3\,\text{s}\) is \(8\,\text{m}\). Since unequal displacements occur in equal time intervals, the motion is non-uniform. The increasing interval displacements suggest that the velocity is increasing during the record.
111. Assertion: A curved \(x-t\) graph represents non-uniform motion.
Reason: The slope of a curved \(x-t\) graph changes from point to point.
ⓐ. Both Assertion and Reason are true, and Reason explains Assertion
ⓑ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓒ. Assertion is true, but Reason is false
ⓓ. Assertion is false, but Reason is true
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: The slope of an \(x-t\) graph represents velocity. A curved \(x-t\) graph does not have the same slope everywhere. Since the slope changes from point to point, the velocity changes with time. Changing velocity is the main feature of non-uniform motion. The Reason directly explains why the Assertion is true in graph language.
112. Use the graph description below.
An \(x-t\) graph starts near the origin and bends upward so that its slope becomes steeper as time increases.
The motion described by this graph has
ⓐ. constant negative velocity
ⓑ. zero velocity at all instants
ⓒ. increasing positive velocity
ⓓ. equal negative displacements in equal time intervals
Correct Answer: increasing positive velocity
Explanation: On an \(x-t\) graph, velocity is represented by the slope. The graph bends upward and becomes steeper with time, so the slope increases. Since the slope is positive and increasing, the velocity is positive and increasing. This is non-uniform motion because the velocity is not constant. The graph shape should not be confused with the physical path; the body is still being described along a straight line.
113. A car covers \(5\,\text{m}\) in the first \(1\,\text{s}\), \(5\,\text{m}\) in the next \(1\,\text{s}\), and \(5\,\text{m}\) in the third \(1\,\text{s}\), all along the same direction. A second car covers \(3\,\text{m}\), \(5\,\text{m}\), and \(7\,\text{m}\) in the same three successive \(1\,\text{s}\) intervals. The correct comparison is
ⓐ. both cars have uniform motion
ⓑ. only the first car has uniform motion
ⓒ. only the second car has uniform motion
ⓓ. neither car has motion because each interval is \(1\,\text{s}\)
Correct Answer: only the first car has uniform motion
Explanation: Uniform motion requires equal displacements in equal time intervals, with the same direction maintained. The first car covers \(5\,\text{m}\) in every \(1\,\text{s}\) interval, so its velocity remains constant. The second car covers \(3\,\text{m}\), then \(5\,\text{m}\), then \(7\,\text{m}\) in equal time intervals. Its displacement per second changes, so its velocity changes. Equal time intervals alone do not guarantee uniform motion; the displacement pattern must also be checked.
114. A body moving on a straight line has positions \(x=0\,\text{m}\), \(x=1\,\text{m}\), \(x=4\,\text{m}\), and \(x=9\,\text{m}\) at \(t=0\,\text{s}\), \(1\,\text{s}\), \(2\,\text{s}\), and \(3\,\text{s}\), respectively. The average velocities in the three successive \(1\,\text{s}\) intervals are
ⓐ. \(1\,\text{m s}^{-1}\), \(3\,\text{m s}^{-1}\), \(5\,\text{m s}^{-1}\)
ⓑ. \(1\,\text{m s}^{-1}\), \(2\,\text{m s}^{-1}\), \(3\,\text{m s}^{-1}\)
ⓒ. \(0\,\text{m s}^{-1}\), \(1\,\text{m s}^{-1}\), \(4\,\text{m s}^{-1}\)
ⓓ. \(3\,\text{m s}^{-1}\), \(3\,\text{m s}^{-1}\), \(3\,\text{m s}^{-1}\)
Correct Answer: \(1\,\text{m s}^{-1}\), \(3\,\text{m s}^{-1}\), \(5\,\text{m s}^{-1}\)
Explanation: \( \textbf{First interval:} \) From \(0\,\text{s}\) to \(1\,\text{s}\),
\[
v_{\text{avg},1}=\frac{1\,\text{m}-0\,\text{m}}{1\,\text{s}}=1\,\text{m s}^{-1}
\]
\( \textbf{Second interval:} \) From \(1\,\text{s}\) to \(2\,\text{s}\),
\[
v_{\text{avg},2}=\frac{4\,\text{m}-1\,\text{m}}{1\,\text{s}}=3\,\text{m s}^{-1}
\]
\( \textbf{Third interval:} \) From \(2\,\text{s}\) to \(3\,\text{s}\),
\[
v_{\text{avg},3}=\frac{9\,\text{m}-4\,\text{m}}{1\,\text{s}}=5\,\text{m s}^{-1}
\]
The average velocity changes from interval to interval.
That change confirms that the motion is non-uniform.
\( \textbf{Final answer:} \) The successive average velocities are \(1\,\text{m s}^{-1}\), \(3\,\text{m s}^{-1}\), and \(5\,\text{m s}^{-1}\).
115. A straight-line motion is described by \(x=t^2\), with \(x\) in \( \text{m} \) and \(t\) in \( \text{s} \). What does this equation suggest about the motion?
ⓐ. Constant velocity because \(x\) is written using \(t\)
ⓑ. Non-uniform motion with unequal displacements
ⓒ. Rest because \(x=0\,\text{m}\) at \(t=0\,\text{s}\)
ⓓ. Negative displacement in every equal interval
Correct Answer: Non-uniform motion with unequal displacements
Explanation: For \(x=t^2\), the position does not increase linearly with time. From \(t=0\,\text{s}\) to \(1\,\text{s}\), \(x\) changes from \(0\,\text{m}\) to \(1\,\text{m}\). From \(t=1\,\text{s}\) to \(2\,\text{s}\), \(x\) changes from \(1\,\text{m}\) to \(4\,\text{m}\), giving a displacement of \(3\,\text{m}\). Equal time intervals therefore do not give equal displacements. A non-linear relation between \(x\) and \(t\) usually indicates a changing velocity.
116. In a non-uniform motion record, why may the average velocity over a long interval fail to describe the velocity at a particular instant?
ⓐ. Because average velocity uses no position information
ⓑ. Because velocity changes during the interval
ⓒ. Because time interval is always negative
ⓓ. Because displacement is always larger than distance
Correct Answer: Because velocity changes during the interval
Explanation: Average velocity gives one overall value for a selected time interval. In non-uniform motion, the velocity changes from one instant to another. A long-interval average can hide these changes because it combines the whole displacement and whole time into one ratio. The velocity at a particular instant requires a more local description. This is why non-uniform motion leads naturally to the idea of instantaneous velocity.
117. A lift first moves slowly upward, then faster upward, along the same vertical line. The best kinematic description is
ⓐ. rest, because the lift remains inside the same shaft
ⓑ. uniform motion, because the path is a straight line
ⓒ. non-uniform one-dimensional motion
ⓓ. two-dimensional motion, because the speed changes
Correct Answer: non-uniform one-dimensional motion
Explanation: The lift moves along a vertical straight line, so one coordinate is enough to describe its position. That makes the motion one-dimensional. However, its speed changes from slow upward motion to faster upward motion. Since the velocity is not constant, the motion is non-uniform. A straight path alone does not guarantee uniform motion; the time pattern of position change also matters.
118. Consider the following statements about uniform and non-uniform motion.
Statement I: Uniform motion has equal displacements in equal time intervals.
Statement II: Non-uniform motion may have a curved \(x-t\) graph.
Statement III: A body moving on a straight line must always have uniform motion.
ⓐ. I and II only
ⓑ. II and III only
ⓒ. I and III only
ⓓ. I, II, and III
Correct Answer: I and II only
Explanation: Statement I is true because constant velocity gives equal displacements in equal time intervals. Statement II is also true because a curved \(x-t\) graph has changing slope, which means changing velocity. Statement III is false because a straight-line path only tells us the geometry of motion. A body can speed up, slow down, or reverse direction while staying on the same straight line. Uniformity depends on how position changes with time, not only on the shape of the path.
119. A moving object has an \(x-t\) graph whose slope decreases but remains positive. The object is
ⓐ. moving in the positive direction with decreasing velocity
ⓑ. moving in the negative direction with increasing velocity
ⓒ. at rest because the slope is changing
ⓓ. moving with constant positive velocity
Correct Answer: moving in the positive direction with decreasing velocity
Explanation: The sign of the slope of an \(x-t\) graph gives the direction of velocity. A positive slope means the object is moving in the positive direction. If the slope decreases with time, the velocity becomes smaller. Since the slope is not constant, the motion is non-uniform. The object is not at rest unless the slope becomes zero.
120. A body covers \(2\,\text{m}\), \(4\,\text{m}\), \(6\,\text{m}\), and \(8\,\text{m}\) in four successive equal time intervals of \(1\,\text{s}\). Its motion is
ⓐ. uniform with velocity \(2\,\text{m s}^{-1}\)
ⓑ. uniform with velocity \(8\,\text{m s}^{-1}\)
ⓒ. non-uniform with increasing speed
ⓓ. rest after the first interval
Correct Answer: non-uniform with increasing speed
Explanation: Each time interval is \(1\,\text{s}\), so the displacement covered in each interval can be compared directly. The successive covered lengths are \(2\,\text{m}\), \(4\,\text{m}\), \(6\,\text{m}\), and \(8\,\text{m}\). These are not equal, so the motion is not uniform. Since the distance covered per second increases, the speed is increasing. This is a simple data-based sign of non-uniform motion.
